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York University

Economics

ECON 4400

Dr.

Summer

Description

Intermediate9LO1 This stock has a constant growth rate of dividends but the required return changes twice To find the value of the stock today we will begin by finding the price of the stock at Year 6 when both the dividend growth rate and the required return are stable forever The price of the stock in Year 6 will be the dividend in Year 7 divided by the required return minus the growth rate in dividends So77PD1gRgD1g Rg350 105 10059850660Now we can find the price of the stock in Year 3 We need to find the price here since the required return changes at that time The price of the stock in Year 3 is the PV of the dividends in Years 4 5 and 6 plus the PV of the stock price in Year 6 The price of the stock in Year 3 is452633 P 3501050 1123501050 112350105 1129850112 3 P 80803Finally we can find the price of the stock today The price today will be the PV of the dividends in Years 1 2 and 3 plus the PV of the stock in Year 3 The price of the stock today is22333P3501050114350105011435010501148080114 0P6346010LO1 Here we have a stock that pays no dividends for 10 years Once the stock begins paying dividends it will have a constant growth rate of dividends We can use the constant growth model at that point It is important to remember that general constant dividend growth formula isPD1gRgttThis means that since we will use the dividend in Year 10 we will be finding the stock price in Year 9 The dividend growth model is similar to the PVA and the PV of a perpetuity The equation gives you the PV one period before the first payment So the price of the stock in Year 9 will bePD Rg1000140511111910 The price of the stock today is simply the PV of the stock price in the future We simply discount the future stock price at the required return The price of the stock today will be9P111111114344011LO1 The price of a stock is the PV of the future dividends This stock is paying four dividends so the price of the stock is the PV of these dividends using the required return The price of the stock is234P101111411118111221114803012LO1 With supernormal dividends we find the price of the stock when the dividends level off at a constant growth rate and then find the PV of the future stock price plus the PV of all dividends during the supernormal growth period The stock begins constant growth in Year 4 so we can find the price of the stock in Year 4 at the beginning of the constant dividend growth asPD1gRg2001051205300044 The price of the stock today is the PV of the first four dividends plus the PV of the Year 3 stock price So the price of the stock today will be2344P1100112800112500112200112300011240090S81

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